Probing the vector charge of Sagittarius A* with pulsar timing

TL;DR

This paper explores how pulsar timing around Sagittarius A* can detect or constrain a hypothetical vector charge in black holes, offering a new way to test alternative gravity theories with future observations.

Contribution

It demonstrates the potential of pulsar timing to detect a vector charge in black holes within the bumblebee gravity model, surpassing current observational constraints.

Findings

A 5-year pulsar observation can constrain the vector charge-to-mass ratio to about 10^{-3}.

Pulsar timing provides more stringent constraints than current EHT observations.

Future pulsar timing could match LISA's prospective constraints on black hole charges.

Abstract

Timing a pulsar orbiting around Sagittarius A* (Sgr A*) can provide us with a unique opportunity of testing gravity theories. We investigate the detectability of a vector charge carried by the Sgr A* black hole (BH) in the bumblebee gravity model with simulated future pulsar timing observations. The spacetime of a bumblebee BH introduces characteristic changes to the orbital dynamics of the pulsar and the light propagation of radio signals. Assuming a timing precision of 1 ms, our simulation shows that a 5-yr observation of a pulsar with an orbital period $P_b\sim 0.5\,{\rm yr}$ and an orbital eccentricity $e\sim 0.8$ can probe a vector charge-to-mass ratio as small as $Q/M\sim 10^{-3}$, which is much more stringent than the current constraint from the Event Horizon Telescope (EHT) observations, and comparable to the prospective constraint from extreme mass-ratio inspirals with the Laser Interferometer Space Antenna (LISA).